How do you integrate $ln(x^(1/3))$ ?

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Answer 1 · 2018-03-19T16:46:13

$1/3xlnx-1/3x+c$

$I=intln(x^(1/3))dx$

using the laws of logs

$I=int 1/3lnxdx$

#

we will integrate by parts

$I=1/3intlnxdx$

$I=intu(dv)/(dx)dx=uv-intv(du)/(dx)dx$

$u=lnx=>(du)/(dx)=1/x$

$(dv)/(dx)=1=>v=x$

$:.I=1/3[xlnx-intx xx 1/xdx]$

$I=1/3[xlnx-intdx]$

$=1/3[xlnx-x]+c$

$1/3xlnx-1/3x+c$

How do you integrate ln(x^(1/3))ln(x^(1/3))?